Fidelity susceptibility and geometric phase in critical phenomenon

doi:10.1088/1674-1056/20/4/040302

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40302-040302.doi: 10.1088/1674-1056/20/4/040302

Fidelity susceptibility and geometric phase in critical phenomenon

田立君¹, 朱长青¹, 秦立国¹, 张宏标²

(1)Department of Physics, Shanghai University, Shanghai 200444, China;Shanghai Key Laboratory for Astrophysics, Shanghai 200234, China; (2)Institute of Theoretical Physics, Northeast Normal University, Changchun 130024, China

收稿日期:2010-11-05 修回日期:2010-12-10 出版日期:2011-04-15 发布日期:2011-04-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11075101), the Shanghai Leading Academic Discipline Project, China (Grant No. S30105), and the Shanghai Research Foundation, China (Grant No. 07d222020).

Fidelity susceptibility and geometric phase in critical phenomenon

Tian Li-Jun(田立君)^a)b)†, Zhu Chang-Qing(朱长青)^a)b), Zhang Hong-Biao(张宏标)^c), and Qin Li-Guo(秦立国)^a)b)

^a Department of Physics, Shanghai University, Shanghai 200444, China; ^bShanghai Key Laboratory for Astrophysics, Shanghai 200234, China; ^c Institute of Theoretical Physics, Northeast Normal University, Changchun 130024, China

Received:2010-11-05 Revised:2010-12-10 Online:2011-04-15 Published:2011-04-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11075101), the Shanghai Leading Academic Discipline Project, China (Grant No. S30105), and the Shanghai Research Foundation, China (Grant No. 07d222020).

摘要/Abstract

摘要： Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We obtain the fidelity susceptibilities for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate (BEC).

关键词: fidelity susceptibility, geometric phase, quantum phase transition

Abstract: Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We obtain the fidelity susceptibilities for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate (BEC).

Key words: fidelity susceptibility, geometric phase, quantum phase transition

中图分类号: (Algebraic methods)

03.65.Fd

03.67.-a (Quantum information) 03.65.Vf (Phases: geometric; dynamic or topological)

田立君, 朱长青, 张宏标, 秦立国. Fidelity susceptibility and geometric phase in critical phenomenon[J]. 中国物理B, 2011, 20(4): 40302-040302.

Tian Li-Jun(田立君), Zhu Chang-Qing(朱长青), Zhang Hong-Biao(张宏标), and Qin Li-Guo(秦立国) . Fidelity susceptibility and geometric phase in critical phenomenon[J]. Chin. Phys. B, 2011, 20(4): 40302-040302.

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Fidelity susceptibility and geometric phase in critical phenomenon

Fidelity susceptibility and geometric phase in critical phenomenon

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